Displaying Polish groups on separable Banach spaces

Details Displaying Polish groups on separable Banach spaces Displaying Polish groups on separable Banach spaces

2011-10-13

arxiv.org/abs/1110.2970v1

Mathematics

Group Theory

27 pages

Scientific paper

A display of a topological group G on a Banach space X is a topological isomorphism of G with the isometry group Isom(X,||.||) for some equivalent norm ||.|| on X, where the latter group is equipped with the strong operator topology. Displays of Polish groups on separable real spaces are studied. It is proved that any closed subgroup of the infinite symmetric group S_\infty containing a non-trivial central involution admits a display on any of the classical spaces c0, C([0,1]), lp and Lp for 1 <=p <\infty. Also, for any Polsih group G, there exists a separable space X on which {-1,1} x G has a display.

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